Replica theory of the rigidity of structural glasses.
ABSTRACT We present a first principle scheme to compute the rigidity, i.e., the shear-modulus of structural glasses at finite temperatures using the cloned liquid theory, which combines the replica theory and the liquid theory. With the aid of the replica method which enables disentanglement of thermal fluctuations in liquids into intra-state and inter-state fluctuations, we extract the rigidity of metastable amorphous solid states in the supercooled liquid and glass phases. The result can be understood intuitively without replicas. As a test case, we apply the scheme to the supercooled and glassy state of a binary mixture of soft-spheres. The result compares well with the shear-modulus obtained by a previous molecular dynamic simulation. The rigidity of metastable states is significantly reduced with respect to the instantaneous rigidity, namely, the Born term, due to non-affine responses caused by displacements of particles inside cages at all temperatures down to T = 0. It becomes nearly independent of temperature below the Kauzmann temperature T(K). At higher temperatures in the supercooled liquid state, the non-affine correction to the rigidity becomes stronger suggesting melting of the metastable solid state. Inter-state part of the static response implies jerky, intermittent stress-strain curves with static analogue of yielding at mesoscopic scales.
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ABSTRACT: We report that the local Debye-Waller factor in a simulated 2D glass-forming mixture exhibits significant spatial heterogeneities and that these short-time fluctuations provide an excellent predictor of the spatial distribution of the long-time dynamic propensities. In contrast, the potential energy per particle of the inherent structure does not correlate well with the spatially distributed dynamics.Physical Review Letters 06/2006; 96(18):185701. · 7.94 Impact Factor
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ABSTRACT: We study the relation of the potential energy landscape (PEL) topography to relaxation dynamics of a small model glass former of Lennard-Jones type. The mechanism under investigation is the hopping between superstructures of PEL minima, called metabasins (MBs). Guided by the idea that the mean durations of visits to MBs should reflect the local PEL structure, we first derive the effective depths of MBs from dynamics, by the relation E(app)=d ln /dbeta, where beta=1/k(B)T. Second, we establish a connection of E(app) to the barriers that surround MBs. As the consequence of a rugged PEL, it turns out that escapes from MBs do not happen by single hops between PEL minima, but correspond to complicated multiminima sequences. We introduce the concept of return probabilities to the bottom of the MBs in order to judge when the attraction range of a MB has been left. The energy barriers overcome can then be identified. These turn out to be in good agreement with the effective depths E(app), calculated from dynamics. We are thus able to relate MB lifetimes to their local structure. Moreover, we can trace back the overall diffusive dynamics to the population of MBs and to their local topology, i.e., to purely thermodynamic and structural quantities. Single energy barriers are identified with the help of a new method, which accurately performs a descent along the ridge between two minima. We analyze the population of transition regions between minima, called basin borders. No indication for the mechanism of diffusion to change around the mode-coupling temperature can be found. We discuss the question whether the one-dimensional reaction paths connecting two minima are relevant for the calculation of reaction rates at the temperatures under study.Physical Review E 03/2003; 67(3 Pt 1):031506. · 2.31 Impact Factor
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ABSTRACT: We present results on a series of two-dimensional atomistic computer simulations of amorphous systems subjected to simple shear in the athermal, quasistatic limit. The athermal quasistatic trajectories are shown to separate into smooth, reversible elastic branches which are intermittently broken by discrete catastrophic plastic events. The onset of a typical plastic event is studied with precision, and it is shown that the mode of the system which is responsible for the loss of stability has structure in real space which is consistent with a quadrupolar source acting on an elastic matrix. The plastic events themselves are shown to be composed of localized shear transformations which organize into lines of slip which span the length of the simulation cell, and a mechanism for the organization is discussed. Although within a single event there are strong spatial correlations in the deformation, we find little correlation from one event to the next, and these transient lines of slip are not to be confounded with the persistent regions of localized shear--so-called "shear bands"--found in related studies. The slip lines give rise to particular scalings with system length of various measures of event size. Strikingly, data obtained using three differing interaction potentials can be brought into quantitative agreement after a simple rescaling, emphasizing the insensitivity of the emergent plastic behavior in these disordered systems to the precise details of the underlying interactions. The results should be relevant to understanding plastic deformation in systems such as metallic glasses well below their glass temperature, soft glassy systems (such as dense emulsions), or compressed granular materials.Physical Review E 08/2006; 74(1 Pt 2):016118. · 2.31 Impact Factor